Course detail

Mathematics 1

FAST-BAA021Acad. year: 2026/2027

Not applicable.

Language of instruction

Czech

Number of ECTS credits

6

Mode of study

Not applicable.

Guarantor

doc. Mgr. Irena Hinterleitner, Ph.D.

Department

Institute of Mathematics and Descriptive Geometry (MAT)

Entry knowledge

Rules for evaluation and completion of the course

Aims

Study aids

Not applicable.

Prerequisites and corequisites

Not applicable.

Basic literature

BUDÍNSKÝ, B. - CHARVÁT, J.: Matematika I. Praha, SNTL, 1987. (CS)
LARSON, R.- HOSTETLER, R.P.- EDWARDS, B.H.: Calculus (with Analytic Geometry). Brooks Cole, 2005. (EN)
STEIN, S. K: Calculus and analytic geometry. New York, 1989. (EN)

Recommended reading

BHUNIA, S. C., PAL, S.: Engineering Mathematics. Oxford University Press, 2015. (EN)
DANĚČEK, J. a kolektiv: Sbírka příkladů z matematiky I. CERM, 2003. (CS)
DANĚČEK, J., DLOUHÝ, O., PŘIBYL, O.: Matematika I. Modul 7 Neurčitý integrál. CERM, 2007. (CS)
DLOUHÝ, O., TRYHUK, V.: Diferenciální počet I. CERM, 2009. (CS)
NOVOTNÝ, J.: Základy lineární algebry. CERM, 2004. (CS)
RYHUK, V. - DLOUHÝ, O.: Modul GA01_M01 studijních opor předmětu GA01. FAST VUT, Brno, 2004. [https://intranet.fce.vutbr.cz/pedagog/predmety/opory.asp] (CS)
SLOVAK, J., PANÁK, M., BULANT, M.: Matematika drsně a svižně. MU Brno, 2013. (CS)

Classification of course in study plans

  • Programme akr_BPC-SIS Bachelor's

    specialization A_SI , 1 year of study, winter semester, compulsory

  • Programme BPC-SIS Bachelor's

    specialization SI , 1 year of study, winter semester, compulsory

Type of course unit

 

Lecture

26 hours, optionally

Teacher / Lecturer

doc. Mgr. Irena Hinterleitner, Ph.D.

Syllabus

  1. Basics of matrix calculus, elementary transformations of a matrix, rank of a matrix.
  2. Determinants (cross rule, Sarrus' rule, Laplace expansion), rules for calculation with determinants.
  3. Vector calculus (operations with vectors, dot, cross, and mixed products of vectors). Real linear space, linear combination and independent bases and dimension of a linear space.
  4. Solutions to systems of linear algebraic equations by Gauss elimination method, Frobenius theorem.
  5. Inverse to a matrix, matrix equations. Eigenvalues and eigenvectors of a matrix.
  6. Real function of one real variable and its basic properties, explicit and parametric definition of a function. Composite function and inverse to a function. Some elementary functions (inverse trigonometric functions). 
  7. Polynomial and the basic properties of its roots, decomposition of a polynomial in the field of real and complex numbers. Rational functions and their decomposition into partial fractions.
  8. Limit of a function, continuous functions, basic theorems.
  9.  Derivative of a function, its geometric and physical applications, rules of differentiation. 
  10.  Differential of a function. Higher-order derivatives, higher-order differentials. Taylor polynomial and Taylor's theorem.
  11. L'Hospital's rule, asymptotes of the graph of a function. Sketching the graph of a function.
  12. Anti-derivative, indefinite integral and its properties. Integration by parts and substitution methods in calculating integrals.
  13. Integration of selected functions (rational, trigonometric, irrational).

Exercise

39 hours, compulsory

Teacher / Lecturer

doc. Mgr. Irena Hinterleitner, Ph.D.

Syllabus

  1. High school repetition.
  2. Basic operations with matrices. Elementary transformations of a matrix, rank of a matrix.
  3. Determinants (cross rule, Sarrus' rule, Laplace expansion), rules for calculation with determinants.
  4. Vector calculus (operations with vectors, dot, cross, and mixed products of vectors).
  5. Solutions to systems of linear algebraic equations by Gauss elimination method.
  6. Inverse to a matrix, matrix equations. Eigenvalues and eigenvectors of a matrix.
  7. Test 1. Some elementary functions (inverse trigonometric functions). Composite function and inverse to a function.
  8. Polynomial and the basic properties of its roots, decomposition of a polynomial in the field of real and complex numbers.
  9. Rational functions and their decomposition into partial fractions. Limit of a function, continuous functions. Derivative of a function, its geometric and physical applications, rules of differentiation.
  10. Differential of a function. Higher-order derivatives, higher-order differentials. Taylor polynomial.
  11. Test 2. L'Hospital's rule, asymptotes of the graph of a function. Sketching the graph of a function.
  12. Anti-derivative, indefinite integral and their properties. Integration by parts and substitution methods in calculating integrals.
  13. Integration of selected functions (rational, trigonometric, irrational).

Individual preparation for an ending of the course

52 hours, optionally

Teacher / Lecturer

doc. Mgr. Irena Hinterleitner, Ph.D.

Self-study

39 hours, optionally

Teacher / Lecturer

doc. Mgr. Irena Hinterleitner, Ph.D.